In this paper we discuss the properties of the reduced density matrix of quantum many body systems with permutational symmetry and present basic quantifications of the entanglement in terms of the von Neumann (VNE). Renyi and Tsallis entropies. In particular we show on the specific example of the spin 1/2 Heisenberg model, how the RDM acquires a block diagonal form with respect to the quantum number k k fixing the polarization in the subsystem conservation of Sz and with respect to the irreducible representations of the Sn group. Analytical expressions for the RDM elements and for the RDM spectrum are derived for states of arbitrary permutational symmetry and for arbitrary polarizations. The temperature dependence and the scaling of the VNE across a finite temperature phase transition is discussed and the RDM moments and the Renyi and Tsallis entropies calculated both for symmetric ground states of the Heisenberg chain and for maximally mixed states.

Reduced density matrix and entanglement entropy of permutationally invariant quantum many body systems - Chap. 9

SALERNO, Mario
2013-01-01

Abstract

In this paper we discuss the properties of the reduced density matrix of quantum many body systems with permutational symmetry and present basic quantifications of the entanglement in terms of the von Neumann (VNE). Renyi and Tsallis entropies. In particular we show on the specific example of the spin 1/2 Heisenberg model, how the RDM acquires a block diagonal form with respect to the quantum number k k fixing the polarization in the subsystem conservation of Sz and with respect to the irreducible representations of the Sn group. Analytical expressions for the RDM elements and for the RDM spectrum are derived for states of arbitrary permutational symmetry and for arbitrary polarizations. The temperature dependence and the scaling of the VNE across a finite temperature phase transition is discussed and the RDM moments and the Renyi and Tsallis entropies calculated both for symmetric ground states of the Heisenberg chain and for maximally mixed states.
2013
978-981-4460-31-6
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/4530258
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact